Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.Self-diffusion in dense rod suspensions are subject to strong geometric constraints because of steric interactions. This topological effect is essentially anisotropic when rods are nematically aligned with their neighbors, raising considerable challenges in understanding and analyzing their impacts on the bulk physical properties. Via a classical Doi-Onsager kinetic model with the Maier-Saupe potential, we characterize the long-time rotational Brownian diffusivity for dense suspensions of hard rods of finite aspect ratios, based on quadratic orientation autocorrelation functions. Furthermore, we show that the computed nonmonotonic scalings of the diffusivity as a function of volume fraction can be accurately predicted by an alternative tube model in the nematic phase.We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of this number N are determined in films with average thicknesses close to 50 and 100 monolayers for a broad range of values of the diffusion-to-deposition ratio R and of the probability ε that lowers the diffusion coefficient for each lateral neighbor. The mobility of subsurface atoms and the energy barriers for crossing step edges are neglected. Simulations show that the adatoms execute uncorrelated diffusion during the time in which they move on the film surface. In a low temperature regime, typically with Rε?1, the attachment to lateral neighbors is almost irreversible, the average number of hops scales as 〈N〉?R^0.38±0.01, and the distribution of that number decays approximately as exp[-(N/〈N〉)^0.80±0.07]. Similar decay is observed in simulations of random walks in a plane with randomly distributed absorbing traps and the estimated relation between 〈N〉 and the density of terrace steps is similar to that observed in the trapping problem, which provides a conceptual explanation of that regime. As the temperature increases, 〈N〉 crosses over to another regime when Rε^3.0±0.3?1, which indicates high mobility of all adatoms at terrace borders. The distributions P(N) change to simple exponential decays, due to the constant probability for an adatom to become immobile after being covered by a new deposited layer. At higher temperatures, the surfaces become very smooth and 〈N〉?Rε^1.85±0.15, which is explained by an analogy with submonolayer growth. Thus, the statistics of adatom hops on growing film surfaces is related to universal and nonuniversal features of the growth model and with properties of trapping models if the hopping time is limited by the landscape and not by the deposition of other layers.In three-dimensional computer simulations of model non-Brownian jammed suspensions, we compute the time required to reach homogeneous flow upon yielding, by analyzing stresses and particle packing at different shear rates, with and without confinement. We show that the stress overshoot and persistent shear banding preceding the complete fluidization are controlled by the presence of overconstrained microscopic domains in the initial solids. Such domains, identifiable with icosahedrally packed regions in the model used, allow for stress accumulation during the shear startup. Their structural reorganization under deformation controls the emergence and the persistence of the shear banding.The dynamic critical behavior of the two-dimensional Ising model with nonextensive Tsallis statistics has been studied. The values of the dynamic critical index z as well as the values of the indices ν and β for different values of the deformation parameter q have been obtained. The emergence of a new type of critical behavior has been revealed.Disordered systems are ubiquitous in physical, biological, and material sciences. Examples include liquid and glassy states of condensed matter, colloids, granular materials, porous media, composites, alloys, packings of cells in avian retina, and tumor spheroids, to name but a few. A comprehensive understanding of such disordered systems requires, as the first step, systematic quantification, modeling, and representation of the underlying complex configurations and microstructure, which is generally very challenging to achieve. Recently, we introduced a set of hierarchical statistical microstructural descriptors, i.e., the "n-point polytope functions" P_n, which are derived from the standard n-point correlation functions S_n, and successively included higher-order n-point statistics of the morphological features of interest in a concise, explainable, and expressive manner. Here we investigate the information content of the P_n functions via optimization-based realization rendering. This is achieved by successively incorporating higher-order P_n functions up to n=8 and quantitatively assessing the accuracy of the reconstructed systems via unconstrained statistical morphological descriptors (e.g., the lineal-path function). https://www.selleckchem.com/products/cc-99677.html We examine a wide spectrum of representative random systems with distinct geometrical and topological features. We find that, generally, successively incorporating higher-order P_n functions and, thus, the higher-order morphological information encoded in these descriptors leads to superior accuracy of the reconstructions. However, incorporating more P_n functions into the reconstruction also significantly increases the complexity and roughness of the associated energy landscape for the underlying stochastic optimization, making it difficult to convergence numerically.Recently, a number of sufficiency conditions have been shown for the occurrence of a Z_2-symmetry breaking phase transition (Z_2-SBPT) starting from geometric-topological concepts of potential energy landscapes. In particular, a Z_2-SBPT can be triggered by double-well potentials, or equivalently by dumbbell-shaped equipotential surfaces. In this paper, we introduce two models with a Z_2-SBPT that, due to their essential feature, show in the clearest way the generating mechanism of a Z_2-SBPT. Although they cannot be considered physical models, they all have the features of such models with the same kind of SBPT. At the end of the paper, the ?^4 model is revisited in light of this approach. In particular, the landscape of one of the models introduced here turned out to be equivalent to that of the mean-field ?^4 model in a simplified version.